# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/779785487:0484
# Permalink to this reading: https://leibnizlegible.com/page/779785487:0484?run=74
# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
# Folio 426, page id 779785487:0484
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=779785487&page=484
# Source image: https://digitale-sammlungen.gwlb.de/content/779785487/jpgs/default/00000484.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 84 lines, status machine
# Lines: 84 recognised, mean confidence 0.89
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

426
PE ZSICE E R ACT. IV.
ctum Phylicum, incellige quaelo progressione quadratorum: Sic enimFig. +.
minimum Phylicum.
PROP. LZ ZZVIIT.
Lumen quod medio radio inest, est
semper et 4. Cum enim lumina
Anc re quadraca dictantiarum, per-
mutando; distantia rlcimi puncti,
est ad distanciam medii puncti, ab
eodem centro sphaera, vE 2. ad 1.
idicur quadraca ve 4. ad 1. igituE
lumen medii, est ad lumen rlcimi,
vc 4. 2d 1. igitur cum lumen rlcimi
Suxponacur semper ve 1. sic enim
vocolumen illud, quo imperte-
Ctius naturaliter produci non po-
rest, cerre lumen medii crit ve 4.
PROP. LXZZIX.
Diniso radio, in quamlibet ratio-
nem cognitam, dici potest, quantum
sit lumen, in puncto, quod segmen-
ta connectit; v. 9. diuidatur radius
juxta rationem =, ica ve Ceomen.
tam versuS CenErUM, AIE L. _ aliud,
Sit VE 2. dico, lumen in puncto
sectionis elle ve 9. cs enim qua-
dracum Cegmenti 1. ad quadratum
Eorius radii 3. vEr. 2d 9. Sed lumi.
na lunc re quadeaca distanciarum,
permutando; hinc punctum cuius
distantia a cenrro est Tubrripla e0.
ejus radii, habet lumen ve 9. si
vero AE Cubquadrup la vF16. s (uB-
quincupla ve 25. (i (excupla vE 36.
quid Eacilius; E vero allumatur
punctum, quod a centro duabus
cerriis dister; lumen illius est ad
lumen vlcimi puncti vrg. ad 4. igi-
EUIE DE 2. 7. 2d 1. Ei vero distet =
eric ve 16. 2d 9. Id cA, VE1. 3. _CC.
PROP. ZC.
Tinc ita dinidi potest radius, et
homina in sectionum punctis; sint in
radius AF, centrum A, vlri.
mum punctum F; aslumaEur AF,
Cubdupla AF, cum AD, Tuberiplas
cum AC, Subquadrupla; cum AB,
Tubquintupla, ecc. dico lum en esle
In F, VE1. In F, VE 4. IN D, rE9.
In C, vE 16. in B, YE 25. eC. vi-
des leriem quadratorum; rario ex
dictis, perlpicua est; nempe lu-
men in F, est ad lumen F, ve qua-
drarum EA, ad quadeacum FA;
id Cst, ver. 2d 4. X ad lumen iir
D, ver. 2d 9. id est, ve quadca-
tum DA, ad quadcarum PA; 8 24
lumen in C, ve quadeacum CA,
ad quadracum FA; id CAE, VE1. 2d
16. Xc. irieur lumina Cune iuX-
ta progrestionem quadtacoru;
_c.
LL+. L2L.
Ita diuidi porest radius, ut lumi-
na proeressionem geomerricam se-
quantur: Sic radius GE; dinidacue
in K, ica ve quadratum HO; sIE
ad LG, VE 1. 2d 2. TUMI IN P, IEa
ve quadeacum IG, (IF 2d quadE2-
eum LO, VE 1. 2d 4. cum in FL, Ica
ve quadratum HIC, sic ad quadra-
EU LG, VF P. ad 8. tum in M, iC2
ve gnadrarum MO, sIc ad quadia-
EUM LO, VE 1. 2d 16. Cerre luMEM
in L Cric 1. In R, 2. in I, 4. In FI,
8. In ML, 16. vides progressionem
Geomerricam duplam; Lunc enirm
lumina re quadrata distanciarum,
Permutando; quomodo; vero F2-
dices huiulmodi quadeaeorum in-
veniantur, vel minimus Tyro in
Geomerria Facilé le le expedier.
ROF